The first degree of quantum involvement, if not opening the door to Thornian time machines, at least seemed to remove some obstacles since quantum fields are known to lead to violations of the energy conditions used in the setting of classical general relativity theory to prove chronology protection theorems and no-go results for time machines.
However, the second degree of quantum involvement seemed, at least initially, to slam the door shut. The intuitive idea was this.
Conclude that the backreaction on the spacetime metric creates unbounded curvature, which effectively cuts off the future development that would otherwise eventuate in CTCs. These intuitions were partly vindicated by detailed calculations in several models. But fortunes were reversed once again by a result of Kay, Radzikowski, and Wald The details of their theorem are too technical to review here, but the structure of the argument is easy to grasp.
The standard renormalization procedure uses a limiting procedure that is mathematically well-defined if, and only if, a certain condition obtains. While the KRW theorem is undoubtedly of fundamental importance for semi-classical quantum gravity, it does not serve as an effective no-go result for Thornian time machines. The KRW theorem functions as a no-go result by providing a reductio ad absurdum with a dubious absurdity: roughly, if you try to operate a Thornian time machine, you will end up invalidating semi-classical quantum gravity.
But semi-classical quantum gravity was never viewed as anything more than a stepping stone to a genuine quantum theory of gravity, and its breakdown is expected to be manifested when Planck-scale physics comes into play. It thus seems that if some quantum mechanism is to serve as the basis for chronology protection, it must be found in the third degree of quantum involvement in gravity.
Both loop quantum gravity and string theory have demonstrated the ability to cure some of the curvature singularities of classical general relativity theory.
An alternative approach to formulate a fully-fledged quantum theory of gravity attempts to capture the Planck-scale structure of spacetime by constructing it from causal sets. Actually, a theorem due to Malament suggests that any Planck-scale approach encoding only the causal structure of a spacetime cannot permit CTCs either in the smooth classical spacetimes or a corresponding phenomenon in their quantum counterparts.
The Time Machine | The Time Machine Wiki | FANDOM powered by Wikia
In sum, the existing no-go results that use the first two degrees of quantum involvement are not very convincing, and the third degree of involvement is not mature enough to allow useful pronouncements. There is, however, a rapidly growing literature on the possibility of time travel in lower-dimensional supersymmetric cousins of string theory. He may be right, but to date there are no convincing arguments that such an Agency is housed in either classical general relativity theory or in semi-classical quantum gravity.
And it is too early to tell whether this Agency is housed in loop quantum gravity or string theory. But even if it should turn out that Hawking is wrong in that the laws of physics do not support a Chronology Protection Agency, it could still be the case that the laws support an Anti-Time Machine Agency. For it could turn out that while the laws do not prevent the development of CTCs, they also do not make it possible to attribute the appearance of CTCs to the workings of any would-be time machine.
Donate to arXiv
Exploring these alternatives is one place that philosophers can hope to make a contribution to an ongoing discussion that, to date, has been carried mainly by the physics community. Participating in this discussion means that philosophers have to forsake the activity of logical gymnastics with the paradoxes of time travel for the more arduous but we believe rewarding activity of digging into the foundations of physics.
Time machines may never see daylight, and perhaps so for principled reasons that stem from basic physical laws. But even if mathematical theorems in the various theories concerned succeed in establishing the impossibility of time machines, understanding why time machines cannot be constructed will shed light on central problems in the foundations of physics.
This conjecture arguably constitutes the most important open problem in general relativity theory. Similarly, as discussed in Section 5, mathematical theorems related to various aspects of time machines offer results relevant for the search of a quantum theory of gravity. In sum, studying the possibilities for operating a time machine turns out to be not a scientifically peripheral or frivolous weekend activity but a useful way of probing the foundations of classical and quantum theories of gravity.
We thank Carlo Rovelli for discussions and John Norton for comments on an earlier draft. Introduction: time travel vs. What is a Thornian time machine? Preliminaries 3. When can a would-be time machine be held responsible for the emergence of CTCs? No-go results for Thornian time machines in classical general relativity theory 5. No-go results in quantum gravity 6. Figure 1. Misner spacetime.
- [gr-qc/] No time machines in classical general relativity!
- Excel 2007 Macros Made Easy.
- The Logics of Biopower and the War on Terror: Living, Dying, Surviving.
Figure 2. Deutsch-Politzer spacetime. Figure 3. A bad choice of initial value surface. Bibliography Arntzenius, F. Zalta ed. Brightwell, G. Dowker, R. Garcia, J. Henson, and R. Chrusciel, P. Hu and T. Jacobson eds.
DeLorean time machine
Cambridge: Cambridge University Press. Davies, P. London: Viking Penguin. Deutsch, D. Earman, J. New York: Oxford University Press. Savitt ed. Goenner, J. Renn, and T. Sauer eds. Smeenk, and C.
DeLorean ("Back to the Future")
Earman, C. Glymour, and J. Stachel eds. Gott, R. New York: Houghton Mifflin.
Greene, B. New York: W. Hawking, S. Sato and T. Nakamura eds. Singapore: World Scientific. Hawking et al. Norton, pp. Hoefer, C. Kay, B. Radzikowski, and R. Keller, S. Krasnikov, S. Piran and R. Ruffini eds. Manchak, J. Monton, B. Morris, M.
go here Thorne, and U. Nahin, P. Norton, J. Ori, A. Politzer, H. Rovelli, C.